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Normal Probability Calculator

THIS PAGE IS A WORK IN PROGRESS

This calculator works the same as NORM.S.DIST(z, cumulative) in Excel. Here, Normal Cumulative Distribution is the same as passing TRUE, while Normal Density is the same as passing FALSE.

Type Z Value

Normal Theory

Normal Distribution refers to any form of continuous data. This could be the length, height, time etc.

Common properties include:

  • Symmetrically distributed
  • Long tails / bell shaped
  • Mean / Mode and Median are the same

Important properties of Normal Distribution are:

  • About 68% of the area under the curve falls within 1 standard deviation of the mean.
  • About 95% of the area under the curve falls within 2 standard deviations of the mean.
  • About 99.73% of the area under the curve falls within 3 standard deviations of the mean.

Normal Tables

When you have a Normal Distribution;

  • The total area under the normal curve = 1.
  • The probability of any particular value is 0.
  • The probability that X is greater than or less than a value = area under the normal curve in that direction.

To create a Standard Normal Distribution from ANY Normal Distribution, you find the z-value. Here, you find how many standard deviations an element is from the mean.

Note that any outliers present within the data will impact variance, standard-deviation, range and average values. Median will NOT be affected.

z = (x - µ) / σ

  • z is the z-score
  • x is the value of the element
  • µ is the population mean
  • σ is the standard deviation

Standard Normal Distribution

The “normal distribution” with mean µ = 0 and variance σ2 = 1, which is denoted as N(0,1) is called the Standard (Unit) Normal Distribution.

The Standard Normal Distribution is much easier to work with and to calculate the area under the curve.

The Standard Normal Cumulative Distribution is tabulated, so you don’t need to perform the calculation yourself, but instead use the tables.

To transform any Normal Distribution fo a Standard (Unit), you simply substitute x for z, where;

z = x - µ ⁄ σ

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